Transistor current gain calculation: A BJT has a DC current gain β = 250. If the base current is IB = 20 µA, what is the collector current IC (assume active region)?

Introduction:In the active region of a BJT, the collector current is approximately proportional to base current via the DC current gain β (also called hFE). This relationship is used to estimate required base drive and to size bias networks for desired collector currents.

Given Data / Assumptions:

• Current gain β = 250.
• Base current IB = 20 µA.
• Transistor operating in active region (not saturated).

Concept / Approach:

The basic relation is IC = β * IB. Multiply the given IB by β, keeping careful track of microampere-to-ampere unit conversions, then express the result in milliamperes for clarity.

Step-by-Step Solution:

Verification / Alternative check:

Reverse check: IB = IC / β = 5 mA / 250 = 0.02 mA = 20 µA, matching the given value. If the transistor were in saturation, IC would be lower than β * IB, but the problem specifies normal operation.

Why Other Options Are Wrong:

• 500 µA: Corresponds to β = 25 or IB = 2 µA, not the given numbers.
• 50 mA: Implies β = 2,500 for IB = 20 µA, unrealistically high.
• 5 A: Six orders of magnitude too large; unit error.
• 2.5 mA: Would require β = 125, not 250.

Common Pitfalls:

• Miscalculating microampere to milliampere conversions.
• Forgetting that β varies with operating conditions; use as a nominal design estimate unless specified.

Final Answer:

5 mA